Method of making skew elements of prestressed concrete

ABSTRACT

This method of producing a skew structures from a reclinear structure without causing its ultimate distortion to impose a stress thereto, consists is applying firstly to said structure, during the storage thereof for curing purposes, a provisional distortion in the same direction as said ultimate distortion but of higher value, thus introducing a stress substantially equal, but in a direction substantially opposite, to that introduced by the distortion necessary for restoring the corresponding structure to the desired ultimate distortion, and subsequently imposing said ultimate distortion to said structure after a suitable time period.

Dec. 25, 1913 C R ON 3,781,401

METHOD OF MAKING SKEW ELEMENTS OF 'FRESTRESSED CON CRETE Filed Jan. 11, 1972 United States Patent 3,781,401 METHOD OF MAKING SKEW ELEMENTS 0F PRESTRESSED CONCRETE Jean Courbon, Tour de Seine, 39 Quai de Grenelle, Paris XV, France Continuation-impart of application Ser. No. 882,586, Dec. 5, 1969. This application Jan. 11, 1972, Ser.

Int. Cl. B28b 21/60 US. Cl. 264-228 5 Claims ABSTRACT OF THE DISCLOSURE BACKGROUND OF THE INVENTION This application is a continuation in part of the application Ser. No. 882,586 filed Dec. 5, 1969, now abandoned.

This invention relates in general to the making of skew or warped structures of prestressed concerte from rectilinear structures without introducing torsion stresses into these structures, and has specific reference to a method of obtaining these skew structures.

Certain prestressed concrete works require sometimes the prefabrication of skew structures which must be made with a high degree of precision, which is rather unusual in public work practice. On the other hand, these skew structures may be repeated in a work with minor difference, although they have very similar geometrical characteristics, as a result of a continuous variation, generally of very small amplitude, of certain parameters.

Such structures can be obtained by using prefabrication beds consisting of standard rectilinear elements, strictly positioned and levelled, which, by resorting to a preliminary adjustment before casting the concrete, will give the desired final neometrical shape, the continuity of the formwork being obtaining by adding selected materials thereto.

The structures thus obtained are subsequently laid, at the end of the concrete setting or curing process, upon suitably levelled permanent bearings, to avoid any subsequent additional distortion. Under these conditions, the concrete is not subjected to any additional stress caused notably by a torsion of the prefabricated structure.

In fact, considering a beam supported by four bearings or supports and not fitted at its ends, it is well known to those conversant with the art that if one of these four supports were put out 'of level, a torque would be created and exerted at both ends of the structure, and that this torque would introduce shearing stresses into the structure which would depend inter alia on the coeflicient of apparent elasticity of the concrete, and would on the other hand be proportional thereto.

These stresses, resulting from a set distortion, not from an external effort, tend to decrease with time as a consequence of the concrete creep.

SUMMARY OF THE INVENTION It is the essential object of the present invention to provide a method of producing skew structures of pre- 3,781,401- Patented Dec. 25, 1973 ice stressed concrete from structures prefabricated on rectilinear beds, in such a manner that the subsequent diflference in level between the bearings in the final permanent position of said structure produces but negligible shearing stresses.

To this end, during the storage of the rectilinear structure for curing purposes a distortion substantially twice that contemplated for the structure supported on its permanent hearings or supports, is applied to said structure, and at the end of said curing period the structure is installed on said ultimate bearings or supports.

The method of the present invention is applied, upon completion of the manufacture of the rectilinear structure, immediately when the concrete strength is sufiicient to permit the stripping and handling thereof without any risk of producing cracks but well before the concrete has cured completely; the method is therefore applied to what is referred to as green concrete.

No external stress or load is applied to the structure and it is only its inherent weight that will produce the structure distortion necessary for causing it to bear on the provisional storage bearings disposed at predetermined levels, such that upon completion of the concrete curing period a skew structure having a predetermined degree of distorsion is obtained.

BRIEF DESCRIPTION OF THE DRAWING The single figure of the attached drawing illustrates by way of example a typical form of embodiment of this invention in case of a structure for the construction of a prestressed concrete track for an airtrain system.

DESCRIPTION OF THE PREFERRED EMBODIMENT The structure 1 is rectilinear and constructed on four coplanar bearings 1, 2, 3 and 4, and then stored as a skew beam supported by'four bearings of which the fourth one 4' is out of level in relation to the other three bearings 1, 2 and 3, so as to apply to the beam a distortion corresponding to twice the distortion to be preserved by the beam when permanently installed on the four bearings, 1, 2, 3 and 4", this fourth bearing 4" being offset in reference to the other three by substantially one-half the difference in level of the intermediate and provisional bearing 4'.

In fact, during the storage for curing purposes, the structure is about two days old and has an apparent instantaneous coefficient of elasticity E(t t of 2X10 t./sq. m., thus introducing a certain shearing stress :7 into the structure. 7 v

After ten days, the deferred coefficient of elasticity of concrete E(t I is 1.5 x10 t./sq. m.; in other words, the remanent stress is'onl3 three fourths of the stress introduced at the storage time 0 a t On the other hand, it is known that at the same age the apparent instantaneous coefficient of elasticity E(t -t of the concrete has increased in reference to the instantaneous coeflicient of elasticity of the two-day old concrete and is 3X10 t./sq. m., thatis, three halves thereof.

When the structure is then installed on its final supports with only a permanent setcorresponding to onehalf of the provisional distortion imposed during the curing phase, this reduction in the distortion corresponds to the application of -a torque in the opposite direction with respect to the torque applied at the beginning of the storage time, this opposite torque being substantially equal to the initial torque after releasing the concrete structure. Therefore, a shearing stress is introduced into the structure:

The sum of these shearing stresses (remanent imposed stress after the cure and stress due to the final positioning) is zero. Therefore, a permanent skew structure having the desired degree of warp has actually been obtained from a. prefabricated rectilinear structure without introducing any shearing stress.

More generally, in the case of structures made from materials for which the coefiicient of elasticity is a function E(t t) of time, t, and of the duration, tt of the load, it is possible to determine a provisional distortion 6 at time t in such a manner that for a final distortion 8 realized at time t no stress is introduced into a struc ture constructed without any initial distortion.

In fact:

(1) The provisional distortion 6 imposed at an age t yields at this age a stress:

0 0 0! 0) (2) at age 1 the remanent stress is (3) if at this age t a distortion 6 is imposed, this new distortion introduces a new stress:

1'= 1 1, '1) whereby the total stress supported by the structure is:

1-I- 1' =K[6 -E(t t )6 E(t no] (4) It will be seen that 5:6 -6 and that 620 if 0 00 1)= 1 1 1) that is, if

As can be seen If E(t t and E(t t are known the provisional distortion 6 to be applied to the structure for obtaining a final distortion 6 without introducing any stress can be determined.

The advantages deriving from the method of this inventron are essentially:

Simplicity, rapidity and economy in the construction of the structure, due to the repeated use of a single mold, even for making structures having a different ultimate warp, provided, of course, that this warp remains within reasonable limits.

Moreover, this method alfords substantial savings in the mrtial design, since it is not necessary to contemplate the use of reinforcing steel bars for supporting the shearng stresses generally encountered in all skew structures in contrast to the method of this invention wherein the ultimate shearing stress caused by the warp is zero. Finally, this method affords a high degree of precision in the manufacture of the skew prestressed concrete elements, s1nce the only requirement is to properly level rmtrally the ultimate and permanent supports on which the structure Is to be laid; besides, the mechanical properties of concrete elements are now known with a sufficrent degree of accuracy, notably regarding the variation in the coefficient of elasticity as a function of time so that the initial distortion to be applied as a function of the desired ultimate or permanent set can also be calculated with a sufiicient degree of precision.

The following procedure may be adhered to, for instance:

The elements are cast in to rectilinear molds (the four bearing points contemplated for this element lying in a common or same plane);

A first steam curing is carried out during about 24 hours until the concrete has attained a strength of the order of 2,900 p.s.i.

In the case of prestressed elements the concrete is prestressed (at about 580 p.s.i.), then stripped from the mold and transferred to the storage site without any risk of producing cracks therein.

Then the elements are stored in such a manner that one of their four bearing points lies above the plane containing the other three, the diiference in level between this one point and the other three or their plane being about +2h, wherein h is the difference in level which it is desired to obtain in the final structure to be obtained with the prefabricated elements.

Under these conditions, the instantaneous coefiicient of elasticity at a time t has the following value:

E -l50,000 bars or 2,175,000 psi.

The final curing of the elements, with this provisional difierence in level between one of their bearing points and the other three, takes about 10 days. It is carried out in a moistened atmosphere (at about humidity contact) and at a temperature of the order of 25 C.

At the end of this 10-day period (time t;) the strength of the concrete element is about 450 bars (6,525 p.s.i.) and its instantaneous coeflicient of elasticity has the following value:

E, -s0o,0oo bars 4,350,000 p.s.i.)

Finally, the elements can be removed from the storage site and used in their final position in the work, the fourth bearing point lying above the plane of the other three but this time with a diiference=h.

Of course, the specific form of embodiment described hereinabove with reference to the attached drawing should not be construed as limiting the field of the invention since many modifications and variations may be brought thereto without departing from the spirit of the present invention.

I have found that it is not possible to state a precise time for beginning the distortion operation due to the many variables involved, a fact well-known to the ordinary Worker in this field. The quality of the cement and notables, its setting rate, the degree of prestress possibly produced therein, the atmospheric or weather conditions (mainly temperature and moisture content of the atmosphere), as well as the other requisite conditions (e.g., steam heating at a more or less elevated temperature) have a considerable influence on the time period which must be allowed to elapse before the distortion can be applied to the concrete element.

What I claim is:

1. A method of obtaining a skew structure of prestressed concrete from a rectilinear structure without causing its ultimate and permanent distortion to develop a stress therein, this method comprising placing concrete in a rectilinear mold, maintaining the concrete in said mold until its strength is sufiicient to permit the application of static post-tensioning forces thereto necessary to prestress the structure, and sufficient to permit the stepping and handling thereof without any risk of producing cracks but well before the concrete has cured completely, immediately applying static tensioning forces to said rectilinear structure, imposing to the thus prestressed rectilinear structure, during its storage for curing purposes, a provisional distortion in the same direction as the desired final distortion but of higher value, so as to introduce into said structure a stress substantiall equal an of opposite direction to that introduced by the distortion necessary for restoring the corresponding structure to the desired permanent set, and then applying at the end of said curing period said desired final distortion to said structure.

2. A method as set forth in claim 1, wherein said provisional distortion imposed to said structure is in the same direction as, and about twice, said desired final distortion.

3. A method according to claim 1 in which the force for the provisional distortion is supplied solely by the weight of the concrete.

4. A method according to claim 1 in which the provisional distortion is applied to the rectilinear structure, as soon as the apparent instantaneous coeflicient 0f elasticity of the concrete is about 2X10 t./sq. m. and the second distortion is applied to the distorted structure when the apparent instantaneous coefficient of elasticity of the concrete is about 3x10 t./sq. m.

5. Method of making from a rectilinear structure of prestressed concrete, a skew structure having in use no stress developed therein, which comprises placing con crete in a rectilinear mold, maintaining the concrete in said mold until its strength is suflicient to permit the application of static post-tensioning forces thereto necessary to prestress the structure, and sufficient to permit the stepping and handling thereof without any risk of producing cracks but well before the concrete has cured completely, immediately applying said static tensioning forces to said rectilinear structure, and providing a plurality of temporary bearings for the thus prestressed rectilinear structure during the storage thereof for concrete curing, at least two of said temporary bearings being co-planar and a further of said temporary bearing being non coplanar, placing said rectilinear structure on said temporary bearings whereby at the beginning of said curing storage the inherent weight of said structure imparts thereto a first predetermined distortion, which is limited by a corresponding further part of said rectilinear structure coming to bear on said further temporary bearing,

said first predetermined distortion being substantially twice that of the skew structure to be made, supporting said distorted structure after the end of the curing storage thereof on at least two co-planar permanent bearings and, at said further part thereof, by a further permanent bearing placed thereunder at about half the distance between the plane of the temporary bearings and the further temporary bearing, whereby a second predetermined distortion is imparted to said structure in use, said first and second distortions being predetermined for the corresponding stresses developed in the structure in use substantially cancelling each other.

References Cited UNITED STATES PATENTS 2,382,139 8/1945 Cueni 264228 2,725,612 12/1955 Lipski 264228 2,920,351 1/1960 Hardesty et a1 264339 2,505,342 4/ 1950 Schaaf 264-71 3,269,424 8/1966 Fisher 264-229 2,796,635 6/1957 Harvender 264--229 ROBERT F. WHITE, Primary Examiner J. R. THURLOW, Assistant Examiner US. Cl. X.R. 

